There is lots of good advice and support here. From the financial perspective alone, I can see where you are coming from. The workload of 5 young children is massive. I certainly understand giving that money to their mother as opposed to a team of babysitters, day care, etc, makes sense.
In my area, many people choose to spend their money "internally" as opposed to spending it on day care. Families, buy larger homes and share with Grandparents, some build in-law suites, some sponsor a relative to move to Canada from overseas. In the end, lots of money get's spent so the children are with people that share the identical values, culture, etc of the parents.
Day care and babysitters have many logistical issues too i.e pick up times, policies re: sick children, splitting children of different ages up, etc.
Daycare has many positives too. To this day I still have friends from the daycare centre D20 went to.
You are not thinking that your $ is a bribe to keep W in your life - we know that. You maybe surrendering a little - but life is about giving and taking.
You are taking a huge step i.e. moving, transfer, etc to what appears to be in pursuit of W. Only you know if that is the case. She will definitely think this is the case.
Take precautions, view this as a exchange of services for $ and a career opportunity for you. With the huge benefit of your children being closer to their mother and her family.
So save some $ for you, build a new support network, continue with your GAL and you and your boys will be fine.
M:50 W:53 MR:20 D:21 S:17 S:11 BD-Sept 2015 Suspected PA Sept 2015-Confronted W & OM Dec 2015 Actually EA In house Sep:Jan/16-May 2016 W moved out:May 22 2016 OM-Intro Oct/17-On scene July/Aug 2017